Wind up doing something refers to what you do in the end, usually after some indecision or discussion. For example, if you weren't sure if you wanted to go watch a movie, or have dinner, you can say:
"We thought about going to the movies, then we realized we were really hungry so we wound up going to a restaurant to eat." [= in the end, we decided to go eat]
"If you continue to smoke so much every day, you're going to wind up in the hospital." [= in the end, you'll get sick and have to be hospitalized]
You can also use "end up."